Difference between revisions of "Conspiracy Number Search"

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=See also=
=See also=
* [[:Category:CNS]]
* [[Alpha-Beta Conspiracy Search]]
* [[Alpha-Beta Conspiracy Search]]
* [[Conspiracy Numbers]]
* [[Conspiracy Numbers]]

Latest revision as of 21:48, 9 September 2020

Home * Search * Conspiracy Number Search

Conspiracy Number Search, (CNS, cns)
a best-first search algorithm first described by David McAllester based on Conspiracy Numbers of the root [2]. Trees are grown in memory - in an often deep and narrow way - that maximizes the conspiracy required to change the root value. The phases of the best-first search procedure are Selection of a leaf node, Expansion and Evaluation of that leaf, and to Back-up the result of that evaluation back to the root.


CNS maintains a range of possible values and keeps expanding the tree until a certain degree of confidence is reached. The confidence is measured by the width of a possible values’ range W and a minimum value for conspiracy numbers T. The purpose of the search is to raise the conspiracy numbers of unlikely values to greater than T in order to reduce the range of possible values to below W. At each turn, CNS tries to disprove either the highest or lowest possible value, which has the highest conspiracy numbers, by expanding one of its conspirators. Then, it recalculates conspiracy numbers and repeats the process until the desired confidence is obtained [3]. Since W depends on the number of possible evaluation values, fine grained evaluation, considered necessary for good positional play, yields into additional computation and thus inefficient search. Further, a final alpha-beta quiescence search in early CNS implementations was quite expensive due to the lack of bounds.


Ulf Lorenz' and Valentin Rottmann's et al. proposed improvements dubbed Controlled Conspiracy Number Search (CCNS) [4] address the drawbacks of CNS by introducing general CN Targets and Extended Conspiracy Numbers. CN targets (security demands) are splitted over the successors in order to inform each node about the goal of its examination. Extended Conspiracy Numbers of the root are defined as the least number of leaf nodes that must change their value in order to change the decision at the root to another move.


Parallel Controlled Conspiracy Number Search (PCCNS) aims at a dynamic distribution of the game tree, initiating a worker/employer relationship along with a sophisticated splitting heuristic of CN targets. The stack, used to keep the nodes of the best-first search, could be manipulated from outside in order to share work and integrate results from other processors [5].

See also

Chess Programs

performing CNS or its improvements:


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External Links

feat.: Jack Gregg, Mark Whitecage, Steve McCall, Gunter Hampel, Sam Rivers, Marty Cook


  1. The Eye of Providence can be seen on the reverse of the Great Seal of the United States, seen here on the US $1 bill. Popular among conspiracy theorists is the claim that the Eye of Providence shown atop an unfinished pyramid on the Great Seal of the United States indicates the influence of Freemasonry in the founding of the United States, Wikimedia Commons
  2. David McAllester (1985). A New Procedure for Growing Minimax Trees. Technical Report, Artificial Intelligence Laboratory, MIT
  3. Quang Vu, Taichi Ishitobi, Jean-Christophe Terrillon, Hiroyuki Iida (2016). Using Conspiracy Numbers for Improving Move Selection in Minimax Game-Tree Search. ICAART 2016, pdf
  4. Ulf Lorenz, Valentin Rottmann, Rainer Feldmann, Peter Mysliwietz (1995). Controlled Conspiracy-Number Search. ICCA Journal, Vol. 18, No. 3
  5. Ulf Lorenz, Valentin Rottmann (1996). Parallel Controlled Conspiracy-Number Search. Advances in Computer Chess 8

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